Abstract
This paper presents new fixed point theorems for 2 Ă— 2 block operator matrix with countably condensing or countably đť““-set-contraction multi-valued inputs. Our theory will then be used to establish some new existence theorems for coupled system of functional differential inclusions in general Banach spaces under weak topology. Our results generalize, improve and complement a number of earlier works.
(Communicated by Michal FeÄŤkan)
References
[1] Ali, A. A.—Ben Amar, A.—O'Regan, D.: Fixed point theorems for the sum of two multivalued mappings and an application to an integral inclusion, Bull. Malays. Math. Sci. Soc. 40 (2017), 1307–1320.10.1007/s40840-015-0110-8Suche in Google Scholar
[2] Ben Amar, A.—Derbel, S.—O'Regan, D.—Xiang, T.: Fixed point theory for countably weakly condensing maps and multimaps in non-separable Banach spaces, J. Fixed Point Theory Appl. 21 (2019), Art. No. 8.10.1007/s11784-018-0644-0Suche in Google Scholar
[3] Ben Amar, A.—Derbel, S.—Boumaiza, M.—O'Regan, D.: Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting, J. Fixed Point Theory Appl. 18 (2016), 327–350.10.1007/s11784-016-0289-9Suche in Google Scholar
[4] Ben Amar, A.—Jeribi, A.—Krichen, B.: Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, Math. Slovaca. 64 (2014), 155–174.10.2478/s12175-013-0193-3Suche in Google Scholar
[5] Boyd, D. W.: On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464.10.1090/S0002-9939-1969-0239559-9Suche in Google Scholar
[6] Cardinali, T.—Papalini, F.: Fixed point theorems for multifunctions in topological vector spaces, J. Math. Anal. Appl. 186 (1994), 769–777.10.1006/jmaa.1994.1332Suche in Google Scholar
[7] Cichon, M.: Weak solution of differential equations in Banach spaces, Discuss. Math. Differ. Incl. 15 (1995), 5–14.Suche in Google Scholar
[8] De Blasi, F. S.: On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. Roumanie 21 (1977), 259–262.Suche in Google Scholar
[9] Dhage, B.C.: Condensing mappings and applications to existence theorems for common solution of differential equations, Bull. Korean Math. Soc. 36 (1999), 565–578.Suche in Google Scholar
[10] Dhage, B. C.: Some generalizations of multi-valued version of schauder's fixed point theorem with applications, Cubo 12 (2010), 139–151.10.4067/S0719-06462010000300009Suche in Google Scholar
[11] Diestel, J.—Uhl, J. J., Jr.: Vector Measures, with a foreword by B. J. Pettis. Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.10.1090/surv/015Suche in Google Scholar
[12] Dobrokov, I.: On representation of linear operators on C0(T, X), Czechoslovak Math. J. 21 (1971), 13–30.10.21136/CMJ.1971.101000Suche in Google Scholar
[13] Fahem, A.—Jeribi, A.—Kaddachi, N.: Existence of solutions for a system of Chandrasekhar’s equations in Banach algebras under weak topology, Filomat 33(18) (2019), 5949–5957.10.2298/FIL1918949FSuche in Google Scholar
[14] Jeribi, A.—Kaddachi, N.—Krichen, B.: Existence results for a coupled system of perturbed functional differential inclusions in Banach algebras, Bull. Malays. Math. Sci. Soc. 41 (2018), 893–918.10.1007/s40840-016-0374-7Suche in Google Scholar
[15] Jeribi, A.—Kaddachi, N.—Krichen, B.: Existence results for a system of nonlinear functional integral equations in Banach algebras under weak topology, Fixed Point Theory 18 (2017), 247–268.10.24193/fpt-ro.2017.1.21Suche in Google Scholar
[16] Jeribi, A.—Kaddachi, N.—Krichen, B.: Fixed-point theorems for multivalued operator matrix under weak topology with an application, Bull. Malays. Math. Sci. Soc. 43 (2020), 1047–1067.10.1007/s40840-019-00724-wSuche in Google Scholar
[17] Jeribi, A.—Krichen, B.: Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory Under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications. Monographs and Research Notes in Mathematics, CRC Press/ Taylor and Francis, 2015.10.1201/b18790Suche in Google Scholar
[18] Jeribi, A.—Krichen, B.—Mefteh, B.: Existence solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations, J. Biol. Dyn. 7 (2013), 218–232.10.1080/17513758.2013.823520Suche in Google Scholar PubMed
[19] Jeribi, A.—Krichen, B.—Mefteh, B.: Fixed point theory in WC-Banach algebras, Turkish J. Math. 40 (2016), 283–291.10.3906/mat-1504-42Suche in Google Scholar
[20] Jeribi, A.—Kaddachi, N.—Laouar, Z.: Fixed point theorems for weakly asymptotically regular mappings in Banach spaces with an application, Numer. Funct. Anal. Optim., to appear.10.1080/01630563.2021.2001820Suche in Google Scholar
[21] Kim, I.-S.: Index formulas for countably k-set contractive operators, Nonlinear Anal. 69 (2008), 4182–4189.10.1016/j.na.2007.10.046Suche in Google Scholar
[22] Kaddachi, N.—Jeribi, A.—Krichen, B.: Fixed point theorems of block operator matrices on Banach algebras and an application to functional integral equations, Math. Methods Appl. Sci. 36 (2013), 659–673.10.1002/mma.2615Suche in Google Scholar
[23] Kaddachi, N.: Existence results of ordinary differential inclusions in Banach algebra under weak topology, J. Phys. Math. 9 (2018), Art. 285.10.4172/2090-0902.1000285Suche in Google Scholar
[24] Kaddachi, N.: Generalized form of fixed point theorems in Banach algebras under weak topology with an application, Filomat 33 (2019), 4281–4296.10.2298/FIL1913281KSuche in Google Scholar
[25] Lech, G.—Ouahab, A.: Some fixed point theorems of a Krasnosel'skii type and application to differential inclusions, Fixed Point Theory 17 (2016), 85–92.Suche in Google Scholar
[26] Mitchell, A. R.—Smith, C.: An existence theorem for weak solutions of differential equations in Banach spaces. Nonlinear Equations in Abstract Spaces (Proc. Internat. Sympos., Univ. Texas, Arlington, Tex., 1977), Academic Press, New York, 1978, pp. 387–403.10.1016/B978-0-12-434160-9.50028-XSuche in Google Scholar
[27] Pettis, B. J.: On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), 277–304.10.1090/S0002-9947-1938-1501970-8Suche in Google Scholar
[28] Taoudi, M. A.—Xiang, T.: Krasnosel'skii type fixed point theorems under weak topology features, Nonlinear Anal. 72 (2010), 478–482.10.1016/j.na.2009.06.086Suche in Google Scholar
[29] Khchine, A.—Maniar, L.—Taoudi, M. A. Krasnosel'skii-type fixed point theorems for convex-power condensing mappings in locally convex spaces, J. Fixed Point Theory Appl. 19 (2017), 2985–3012.10.1007/s11784-017-0465-6Suche in Google Scholar
[30] Ursescu, C.: Multifunctions with convex closed graph, Czechoslovak Math. J. 25 (1975), 438–441.10.21136/CMJ.1975.101337Suche in Google Scholar
© 2021 Mathematical Institute Slovak Academy of Sciences
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Artikel in diesem Heft
- Regular Papers
- Semidistributivity and Whitman Property in implication zroupoids
- Composition of binary quadratic forms over number fields
- On Z-Symmetric Rings
- On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences
- Coefficient estimates for Libera type bi-close-to-convex functions
- Oscillation of nonlinear third-order differential equations with several sublinear neutral terms
- On rapidly oscillating solutions of a nonlinear elliptic equation
- Multiplicity of solutions for a class of fourth-order elliptic equations of p(x)-Kirchhoff type
- Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities
- On absolute double summability methods with high indices
- On the continuity of lattice isomorphisms on C(X, I)
- New fixed point theorems for countably condensing maps with an application to functional integral inclusions
- Common fixed point results under w-distance with applications to nonlinear integral equations and nonlinear fractional Differential Equations
- The form of locally defined operators in waterman spaces
- Conformal vector fields on almost co-Kähler manifolds
- A certain η-parallelism on real hypersurfaces in a nonflat complex space form
- On log-bimodal alpha-power distributions with application to nickel contents and erosion data
- Univariate and bivariate extensions of the generalized exponential distributions
- Pellian equations of special type